requires considerable strength; such as windlasses on board ship. Each single stroke of the click-arms advances the ratchet through one-half of its pitch.

Corresponding points in the two figures are marked with the same letters; and as fig. 148 contains some parts which do not

occur in fig. 149, the former will, in the first place, be referred to in explaining the principles to be followed in designing such combinations.

Let the figure and dimensions of the ratchet-wheel be given, and let A be its axis, and B B its pitch-circle; that is, a circle midway between the points and roots of the teeth.

Having fixed the mean obliquity of the action of the clicksthat is, the angle which their lines of action, at mid-stroke, are to make with tangents to the pitch-circle-draw any convenient radius of the pitch-circle, as L A, and from it lay off the angle L A D, equal to that obliquity. On A D let fall the perpendicular L D, and with the radius A D describe the circle CC; this will be the base-circle, to which the lines of action of the clicks are to be tangents. (As to base-circles, see also Article 131, page 121.) Lay off the angle D A E equal to an odd number of times half the pitchangle; then through the points D and E in the base-circle draw two tangents, cutting each other in F. Draw F G, bisecting the angle

at F, and take any convenient point in it, G, for the trace of the axis of motion of the rocking-shaft which carries the click-arms. From G let fall G H

and G K perpendicular to the tangents FDH and EF K; then H and K will be the positions of the centres of motion of the two clicks at midstroke; and G H and FK will represent the click-arms. Let L and M be the points where DH and E K respectively cut the pitchcircle; then H L and K M will be the lengths of the two clicks. The effective stroke of each click will be equal to half the pitch, as measured on the base-circle C C; and the total stroke must be as much greater as is necessary in order to make the clicks clear the teeth.

B

A

Fig. 149.

K

In fig. 149, where the clicks pull instead of pushing, the obliquity is nothing; and the consequence is that the base-circle, C C, coincides with the pitch-circle, B B, and that the points L and M coincide respectively with D and E.

197. Frictional Catch.-The frictional catch (called sometimes. the "silent feed-motion") is a sort of intermittent linkwork, founded on the dynamical principle, that two surfaces will not slide on each other so long as the angle which the direction of the pressure exerted between them makes with their common normal at the place where they touch each other is less than a certain angle called the angle of repose, which depends on the nature of the surfaces, and their state of roughness or smoothness, and of lubrication. The smoother and the better lubricated the surfaces, the smaller is the angle of repose.

In trigonometrical language, the angle of repose is the angle whose tangent is equal to the co-efficient of friction: that is, to the ratio which the friction between two surfaces, being the force which resists sliding, bears to the normal pressure; or, what is the same thing, it is the angle whose sine is equal to the ratio that the friction bears to the resultant pressure when sliding takes place. The subject of friction, and of the angle of repose, properly belong to the dynamical part of this treatise, and will be mentioned in greater detail further on. For the present purpose it is sufficient to state that the sine of the angle of repose for metallic surfaces in a

moderately smooth state, and not lubricated, as deduced from the experiments of Morin, ranges from 0.15 to 0.2, or thereabouts; so

that an angle whose sine is one-seventh of radius may be considered to be less than the angle of repose of any pair of metallic surfaces which are in the above-mentioned condition.

The frictional catch, though always depending on the principle just stated, is capable of great variety in detail. The arrangement represented in fig. 150 is constructed in the following man

ner:

The shaft and rim of the wheel to be acted upon are shown in section. A K is the catch-arm, having a rocking motion about the axis A of the wheel; the link by which it is driven is supposed to be jointed to it at K; and K' K" represents the stroke, or arc of motion, of the point

L is

K; so that K'A K" is the angular stroke of the catch-arm. a socket, capable of sliding longitudinally on the catch-arm to a small extent; a shoulder for limiting the extent of that sliding motion is marked by dotted lines. The socket and the part of the arm on which it slides should be square, and not round, to prevent the socket from turning. From the side of the socket there projects a pin at D, from which the catch D G H hangs. M is a spring, pressing against the forward side of the catch. G and H are two studs on the catch, which grip and carry forward the rim, B B C C, of the wheel during the forward stroke, by means of friction, but let it go during the return stroke.

A similar frictional catch, not shown in the figure, hanging from a socket on a fixed instead of a moveable arm, at any convenient part of the rim of the wheel, serves for a detent, to hold the wheel still during the return stroke of the moveable catch-arm.

The following is the graphic construction for determining the proper position of the studs G and H-Multiply the radii of the outer and inner surfaces, B B and C C, of the rim of the wheel by a co-efficient a little less than the sine of the angle of repose-say -and with the lengths so found as radii describe two circular arcs about A; the greater (marked E) lying in the direction of forward motion, and the less (marked F) in the contrary direction. From D, the centre of the pin, draw D E and D F, touching those two arcs. Then G, where D E cuts B B, and H, where D F cuts C C, will be the proper positions for the points of contact of the two studs with the rim of the wheel. For the force by which the catch is driven during the forward stroke acts through D; that force is resolved into two components, acting along the lines D GE and F H D respectively; and those lines make with the normals to the rim of the wheel, at G and H respectively, angles less than the angle of repose of a pair of metallic surfaces that are not lubricated. Should it be thought desirable, the positions of the holding studs, or of one of them, may be made adjustable by means of screws or otherwise.

The stiffness of the spring M ought to be sufficient to bring the catch quickly into the holding position at the end of each return stroke.

The length of stroke of a frictional catch is arbitrary, and may, by suitable contrivances, be altered during the motion. Contrivances for that purpose will be described further on.

A pair of frictional catches may be made double-acting, like the double-acting clicks of the preceding Article.

198. Slotted Link.—A slotted link is connected with a pin at one of its ends, not by a round hole fitting the pin closely, but by an oblong opening or slot with semicircular ends. This is an example of intermittent linkwork; the intermission in its action taking place during the middle part of each stroke, while the pin is shifting its position relatively to the link from the one end of the slot to the other. That intermission takes effect by producing a pause in the motion of that piece which is the follower, and which may be either the link or the pin; and the stroke of the follower is shorter than that of the driver by an extent corresponding to the length of the slot, as measured from centre to centre of its two semicircular ends.

199. Band Links.-Where tension alone, and not thrust, is to act along a link, it may be flexible, and may consist either

A

of a single band, or of an endless band passing round a pair of pulleys which turn round axes traversing and moving with the connected points. For example, in fig. 151, A is the axis of a rotating shaft, B that of a crank-pin, C the other connected point, and B C the line of connection; and the connection is effected by means of an endless band, passing round a pulley which is centred upon C, and round the crank-pin itself, which acts as another pulley. The pulleys are of course secondary pieces; and the motion of each of them belongs to the subject of aggregate combinations, being compounded of the motion which they have along with the line of connection, B C, and of their respective rotations relatively to that line as their line of centres; but the motion of the points B and C is the same as if B C were a rigid link, provided that forces act which keep the band always in a state of tension.

Fig. 151

This combination is used in order to lessen the friction, as compared with that which takes place between a rigid link and a pair of employed is often a leather chain, of the kind already mentioned in Article 176, page 191, because of its flexibility.

pins; and the band

SECTION VII.-Connection by Plies of Cord, or by

Reduplication.

200. General Explanations. (A. M., 494.)—The combination of pieces connected by the several plies of a cord, rope, or chain, consists of a pair of cases or frames called blocks, each containing one or more pulleys called sheaves. One of the blocks (A, figs. 152, 153), called the fixed block, or fall-block, is fixed; the other, called the Ay-block, or running block, B, is moveable to or from the fallblock, with which it is connected by means of a rope, or fall, of which one end is fastened either to a fixed point or to the running block, while the other end, C, called the hauling part, is free; and the intermediate portion of the rope passes alternately round the pulleys in the fixed block and running block. The several plies of the rope are called by seamen parts; and the part which has its end fastened is called the standing part. The whole combination is called a tackle or purchase. When the hauling part is the driver, and the running block the follower, the two blocks are being drawn